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The graph of a cosine function shows a reflection over the x-axis, an amplitude of 2, a period of 4, and a phase shift of 0.5 to the right.

Which is the equation of the function described?

f(x)=−2cos(πx/2−π/2)

f(x)=−2cos(πx−1/2)

f(x)=−2cos(πx−1/4)

f(x)=−2cos(πx/2−π/4)

 Mar 12, 2021
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We  have

 

y = Acos (Bx  + C)  

 

A = the  amplitude =  2

Since  this is  reflected over  the x axis, we  have    A  = -2

 

B =   2pi  /  period  =   2pi  / 4  =   pi/2

 

To  find C  ....the point (.5, -2)  is on the  graph   ....so.....

 

-2  = -2cos (pi * .5  / 2   +  C)            divide through  by  -2

 

1 =  cos ( pi *.5 / 2  +  C)

 

1 =  cos ( pi/4 + C)

 

arccos(1)  = pi/4  + C

 

0  =  pi/4 + C

 

C  = - pi/4

 

The  function is

 

f(x) = -2cos ( pi * x / 2  - pi/4  )

 

Here's a graph :  https://www.desmos.com/calculator/eqbmyly3sk

 

 

cool cool cool

 Mar 12, 2021
edited by CPhill  Mar 12, 2021

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